Mass Spectrometers (MS), as widely applied chemical analysis instruments, have been applied in various fields. In a certain mass spectrometer, in the ion source portion, a substance gets or loses charges (ionization) by various means and becomes charged ions. Then, charged ions with a different mass-to-charge ratio are filtered in accordance with different principles and then reach a detector. In this way, a mass spectrum is obtained. In the mass spectrometry, there are many ionization techniques: Electron Ionization (EI) and Chemical Ionization (CI) for the gas chromatography-mass spectrometry, and Electrospray Ionization (ESI) and Atmosphere Pressure Chemical Ionization (APCI) and the like for the liquid chromatography-mass spectrometry.
The analysis of the mass spectrum, especially the analysis of the mass spectrum of unknown substances, is very important. The existing various mass spectrometric data is to be analyzed by various experiences. For example, in EI-MS which is mainly used for detecting volatile substances, molecular ion peaks may be found by several rules (for example, Nitrogen Rule), and then the mass spectrometric peaks of various fragments are deduced according to the isotope and energy rules, and finally the structures of the substances represented by the mass spectrums are obtained. There are many unknown components in natural products and traditional Chinese medicines. On the other hand, in EI-MS, for known substances, the mass spectrums and the mass spectrometric database (for example, NIST database) are mainly used for comparison to obtain the structural information about the components in the existing techniques. However, for traditional Chinese medicines with complicated components, since there are many isomeric components therein, most fragments in their mass spectrums have the same position, only different in abundance in some places. In this case, it is even difficult to determine a certain isomer by comparing the mass spectrum of a pure substance with the NIST database.
In the liquid chromatography-mass spectrometry (ESI-MS, APCI-MS, etc.) and solid chromatography-mass spectrometry, usually, during the electrification, the substances will not break, and instead, will form complexes together with some ions (Na+, K+, H+) or even form polymers and have several charges. Therefore, in the liquid chromatography-mass spectrometry, it is very difficult to determine which compound the substance is by the mass spectrometric peak in the first-stage mass spectrometry (MS1). Instead, it is able to determine the information about a compound represented by one mass spectrometric peak only, by multi-stage fragmentation using multi-stage mass spectrometry (MSn).
In the existing mass spectrum analysis, the analysis of the mass spectrum is a very professional subject. Although there have been many rules for analysis, only few people are proficient in this because of high requirements on the desired subject knowledge and coverage of a wide range of knowledge. The existing analysis of the mass spectrum is costly due to these reasons. Thus, the application of the analysis of the mass spectrum is restricted.
In the mass spectrometry, the ionization and fragmentation of molecules in the ion source of the mass spectrometer is a very complicated process in which various different ions are generated. The process of ion fragmentation in the mass spectrometry is a complicated reaction process. The ion fragmentation rule in the mass spectrometry is influenced by the mass spectrometry itself and the environment. The generated molecular ions and fragment ions are influenced by their own structure and the internal energy, and also influenced by the charge generation process and the environment. For example, the kinetic process of ion fragmentation can be influenced by all the EI voltage, degree of vacuum and ion accelerating voltage. In the mass spectrometry, the ion generation process is very short, roughly only about 10 milliseconds. Therefore, experimentally, it is very difficult to capture the ion fragmentation process. The common method is to analyze by the method of quantum mechanics. There has been no report on the studies on the kinetic process of ion fragmentation in the mass spectrometry by other methods.
Various mathematical methods have been widely used in analytical instruments and various analysis methods, to aid in solving various problems in the analysis, for example, the problem of baselines. Those mathematical methods are collectively called stoichiometry. It is a subject worthy of study to analyze the fragmentation processes (kinetic processes) of those ions in the mass spectrometry by stoichiometry.
It is significant meaningful to smoothly understand the fragmentation process of ions in the mass spectrometry, which can help the researchers to find new compounds more quickly and easily, better understand the structural information of various types of compounds, distinguish between similar compound structures (for example, isomers) by the obtained kinetic information, and better determine the nature of substances.
Independent Components
Independent components refer to certain components, functional groups or fragments in the mixtures, the behavior pattern of which is free of the interference of other components, functional groups or fragments. The behavior pattern of those independent components remains consistent and varying. Although the detected amplitude (for example, abundance) changes because of the change in their concentration, their features (for example, pure spectrum) remain unchanged. For example, in the mass spectrum of a mixture, the independent components may be pure components in the mixture, and the pure spectrum of the independent components remains consistent at different sampling times without being influenced by other components. During the ion fragmentation of a pure substance in the mass spectrometry, the independent components may be certain individual charged functional groups or fragments. Since the independent components have constant mass and composition, their mass spectra (including isotopic peaks) are also constant. When explained mathematically, the comprehensive presentation of a complex containing many independent components is the linear summation of the independent components, i.e., the linear system. The actual linear system will be somewhat different from the linear system because of the involved processes such as electronic sampling and data processing, and various noises.
Entropy Minimization Algorithms
Stoichiometry and chemical dynamics belong to two subjects. Amongst other things, stoichiometric methods, i.e., the entropy minimization algorithms, are used for the discovery of intermediate products of chemical reactions and the analysis of mixed spectra. Entropy minimization algorithms (EMs) were developed on the basis of Shannon Entropy. Shannon Entropy was originally published in 1948 [C. E. Shannon, The Bell System Technical Journal, 27 (1948) 379-423]. It is an academic term in the field of information, for measuring the uncertainty of random parameters.
Marc Garland is the first one who found the application of Shannon Entropy in chemical analysis [Y. Z. Zeng, M. Garland, Analytica Chimica Acta, 359 (1998) 303-310]. He published BTEM (Band-Target Entropy Minimization) in 2002 [W. Chew, E. Widjaja, M. Garland, Organometallics, 21 (2002) 1982-1990]. In this method, the infrared spectrum of reactants and resultants in a certain closed reaction system is reconstructed by using the entropy minimization algorithm by studying the closed reaction system and performing infrared data sampling at different reaction time.
Although the kinetic process of the reaction can be studied by the entropy minimization algorithms, those methods are mainly used for reconstructing the pure spectra of components from the mixed spectra. In 2003, H. J. Zhang et al. published the tBTEM (Weighted Two-Band Target Entropy Minimization) [H. J. Zhang, M. Garland, Y. Z. Zeng, P. Wu, J Am Soc Mass Spectrom, 14 (2003) 1295-1305]. This method is mainly used for the analysis of mass spectra. In 2006, H. J. Zhang et al. published the MREM (Multi-Reconstruction Entropy Minimization) [H. J. Zhang, W. Chew, M. Garland, Applied Spectroscopy, 61 (2007) 1366-1372]. In this method, the global optimization is replaced with the local optimization, and no search range is to be specified manually. The function of automatically searching for pure spectra is truly realized.
In 2009, the entropy minimization algorithms were eventually applied to the analysis of ultraviolet spectra [F. Gao, H. J. Zhang, L. F. Guo, M. Garland, Chemometrics and Intelligent Laboratory Systems, 95 (2009) 94-100].